Math Words with Multiple Meanings

July 29, 2008

Lesson Question:

How can the Visual Thesaurus help students better understand the language of mathematics?

Applicable Grades:

3-12

Lesson Overview:

In this lesson, small groups of students will use the Visual Thesaurus to explore the multiple meanings of some common math terms. Then, groups will synthesize this knowledge by coming up with examples of the words in both mathematical and other contexts.

Length of Lesson:

One hour to one hour and a half

Instructional Objectives:

Students will:

write mathematical and verbal expressions

identify the multiple meanings of some common math terms

share examples of words being used in both mathematical and other contexts

Materials:

Warm-up:

Brainstorming expressions in English and in Math:

Organize the class in small groups and explain that each group is about to receive a simple set of instructions written on an index card. They are to follow the instructions without consulting with you or with students in other groups.

Distribute to half of the groups in the classroom index cards with the following instructions written on the cards: "English assignment: Come up with an expression containing a product."

Distribute index cards to the other groups in the classroom with the following set of instructions: "Math assignment: Come up with an expression containing a product."

Give students a few minutes to confer with their fellow group members and to collectively write an expression in their notes or on the back of the index card.

Instruction:

Eliciting verbal and mathematical expressions:

Elicit a few groups' expressions and write them on the board. Make sure you include at least one verbal expression and one mathematical expression. For example, groups with the "English assignment" most likely wrote verbal expressions that somehow included a product's name (e.g., My heart keeps on ticking like a Timex watch), and groups with the "Math assignment" most likely wrote algebraic expressions involving multiplication [e.g., 2x = 10 (answer: x = 5)].

Reveal to the class that all of the groups received the same set of instructions (i.e., "come up with an expression containing a product"), but the context of each set of instructions differed (i.e., English vs. Math).

Using the VT to define content-specific language:

Ask students to identify the words in the instructions that were interpreted differently in the two contexts (i.e., expression and product), and then show the class the VT word web displays for expression and product on the white board.

Have students identify the meanings in the word web displays for expression and product that are specific to a mathematical context (i.e., expression: "a group of symbols that make a mathematical statement"; product: "a quantity obtained by multiplication").

Point out that sometimes words can have multiple "content-specific" meanings. In this case, expression and product have specific meanings in a mathematical context, but these words have entirely different meanings in other contexts (e.g., an expression can mean a saying or a facial expression; a product can mean merchandise or a result, etc.).

Identifying multiple meanings of some basic math terms:

Distribute a "Math Words with Multiple Meanings" chart to each group [click here to download] and explain that the left-hand column of the chart contains a list of words that have both math-specific meanings and multiple other meanings in different "non-math" contexts.

Explain to groups that it will be their job to look each term up on the VT and provide one math-specific example for the word and one example of how that same word could be used in another context. For example, the first entry was inspired by Debbie Shults's rhetorical question "Is a meter in poetry the same as a meter in math class?" [click here to download Shults's VT article "Vocabulary Instruction: The Non-Amorphous Shape of Word Knowledge."] (As you can see in the example entry, one type of meter can be used to measure the perimeter of a square, whereas another type of meter is used to describe "the accent in a metrical foot of verse.")

Give groups ample time to use the VT to explore the multiple meanings of each math term included on the chart and to provide examples of each word in a mathematical context and in another context. Inform students that their examples in the "Mathematical Context" column do not have to be verbal examples. For example, an example for angle could be an illustration of a geometric angle or an example for parallel could be a drawing of two parallel lines.

Wrap-up:

Sharing examples:

If you do not have time to have each group present its examples from their completed charts, you could quickly reconfigure the groups in a "jigsaw fashion" so that each new group could be made up of students from different previous groups. In this way, students could share their examples and be exposed to the variety of ways each word can be interpreted.

If time permits, you could discuss if there is some overlap or connection between the mathematical meanings of words and their other meanings. For example, how does the mathematical definition of parallel lines relate to the use of the word parallel to describe parallel lives?

Extending the Lesson:

One fun way to extend this lesson would be to have students create a math glossary based on their research with the VT as they completed the "Math Words with Multiple Meanings" chart. The glossary could be written in a casual "student to student" style where writers attempt to explain each term in their own words for their peers.

Assessment:

Groups' completed "Math Words with Multiple Meanings" charts should be assessed by checking to see that each row accurately reflects the appropriate usage of a word in a mathematical context and in another context.

Students' understanding of the math vocabulary contained in the "Math Words with Multiple Meanings" chart could be easily assessed by giving the class a "math vocabulary quiz" to see if students can correctly match math terms with examples of those terms.

Educational Standards:

Mathematics

Standard 2. Understands and applies basic and advanced properties of the concepts of numbers

Level III (Grades 6-8)

1. Understands the relationships among equivalent number representations (e.g., whole numbers, positive and negative integers, fractions, ratios, decimals, percents, scientific notation, exponentials) and the advantages and disadvantages of each type of representation

2. Understands the characteristics and properties (e.g., order relations, relative magnitude, base-ten place values) of the set of rational numbers and its subsets (e.g., whole numbers, fractions, decimals, integers)

3. Understands the role of positive and negative integers in the number system

Standard 5. Uses the general skills and strategies of the reading process

Level III (Grades 6-8)

2. Uses word origins and derivations to understand word meaning (e.g., Latin and Greek roots and affixes, meanings of foreign words frequently used in the English language, historical influences on English word meanings)